The density of the core of a planet is ρ 1 and that of the outer shell is ρ 2 , the radii of the core and that of the planet are R and 2R respectively. The acceleration due to gravity at the surfa

Question

The density of the core of a planet is ρ 1 ​ and that of the outer shell is ρ 2 ​ , the radii of the core and that of the planet are R and 2R respectively. The acceleration due to gravity at the surface of the planet is same as at a depth R. Find the value of ρ 2 ​ 3 ρ 1 ​ ​ .

TestHub · Accepted Answer

Let m1 be the mass of the core and m 2 ​ the mass of outer shell g A ​ = g B ​ (given) Then, R 2 Gm 1 ​ ​ = ( 2 R ) 2 G ( m 1 ​ + m 2 ​ ) ​ ∴ 4 m 1 ​ = ( m 1 ​ + m 2 ​ ) or 4 { 3 4 ​ π R 3 ρ 1 ​ } = 3 4 ​ π R 3 . ρ 1 ​ + { 3 4 ​ π ( 2 R ) − 3 4 ​ π R 3 } r 2 ​ ∴ 4 ρ 1 ​ = ρ 1 ​ + 7 ρ 2 ​ ∴ ρ 2 ​ ρ 1 ​ ​ = 3 7 ​

Physics - Gravitation Question with Solution | TestHub

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